High-Order Finite-Differences Schemes to Solve Poisson's Equation in Polar Coordinates

In the present work finite difference schemes of second andfourth order are derived for the solution of Poisson's equationin polar coordinates. To solve the resulting system of linearequations, a direct method similar to Hockney's method is developed.The schemes are tested on six test problems whose exact solutionsare known. The numerical results obtained by these finite-differenceschemes show that they produce very accurate results.